Question: Graph this system of equations and solve. $6x-5y = -10$ $2x-10y = 30$ $1$ $2$ $3$ $4$ $5$ $6$ $7$ $8$ $9$ $10$ $\llap{-}2$ $\llap{-}3$ $\llap{-}4$ $\llap{-}5$ $\llap{-}6$ $\llap{-}7$ $\llap{-}8$ $\llap{-}9$ $\llap{-}10$ $1$ $2$ $3$ $4$ $5$ $6$ $7$ $8$ $9$ $10$ $\llap{-}2$ $\llap{-}3$ $\llap{-}4$ $\llap{-}5$ $\llap{-}6$ $\llap{-}7$ $\llap{-}8$ $\llap{-}9$ $\llap{-}10$ Click and drag the points to move the lines.
Convert the first equation, $6x-5y = -10$ , to slope-intercept form. $y = \dfrac{6}{5} x + 2$ The y-intercept for the first equation is $2$ , so the first line must pass through the point $(0, 2)$ The slope for the first equation is $\dfrac{6}{5}$ . Remember that the slope tells you rise over run. So in this case for every $6$ positions you move up You must also move $5$ positions to the right. $5$ positions to the right. $6$ positions up from $(0, 2)$ is $(5, 8)$ Graph the blue line so it passes through $(0, 2)$ and $(5, 8)$ Convert the second equation, $2x-10y = 30$ , to slope-intercept form. $y = \dfrac{1}{5} x - 3$ The y-intercept for the second equation is $-3$ , so the second line must pass through the point $(0, -3)$ The slope for the second equation is $\dfrac{1}{5}$ . Remember that the slope tells you rise over run. So in this case for every $1$ position you move up You must also move $5$ positions to the right. $5$ positions to the right. Graph the green line so it passes through $(0, -3)$ and $(5, -2)$ The solution is the point where the two lines intersect. The lines intersect at $(-5, -4)$.